Simplify the following expression: $\dfrac{32t^2}{48t}$ You can assume $t \neq 0$.
Explanation: $ \dfrac{32t^2}{48t} = \dfrac{32}{48} \cdot \dfrac{t^2}{t} $ To simplify $\frac{32}{48}$ , find the greatest common factor (GCD) of $32$ and $48$ $32 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2$ $48 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3$ $ \mbox{GCD}(32, 48) = 2 \cdot 2 \cdot 2 \cdot 2 = 16 $ $ \dfrac{32}{48} \cdot \dfrac{t^2}{t} = \dfrac{16 \cdot 2}{16 \cdot 3} \cdot \dfrac{t^2}{t} $ $\phantom{ \dfrac{32}{48} \cdot \dfrac{2}{1}} = \dfrac{2}{3} \cdot \dfrac{t^2}{t} $ $ \dfrac{t^2}{t} = \dfrac{t \cdot t}{t} = t $ $ \dfrac{2}{3} \cdot t = \dfrac{2t}{3} $